An Efficient Consistency Algorithm for the Temporal Constraint Satisfaction Problem

Dechter et al. [5] proposed solving the Temporal Constraint Satisfaction Problem (TCSP) by modeling it as a meta-CSP, which is a finite CSP with a unique global constraint. The size of this global constraint is exponential in the number of time points in the original TCSP, and generalized-arc consistency is equivalent to finding the minimal network of the TCSP, which is NP-hard. We introduce _AC, an efficient consistency algorithm for filtering the meta-CSP. This algorithm significantly reduces the domains of the variables of the meta-CSP without guaranteeing arc-consistency. We use _AC as a preprocessing step to solving the meta-CSP. We show experimentally that it dramatically reduces the size of a meta-CSP and significantly enhances the performance of search for finding the minimal network of the corresponding TCS

Techniques for Bundling the Solution Space of Finite Constraint Satisfaction Problems

We study the backtrack-search procedure with forward checking (FCBT) for finding all solutions to a finite Constraint Satisfaction Problem (CSP). We describe how to use dynamic interchangeability to enhance the performance of search and represent the solution space in a compact manner. We evaluate this strategy (FC-DNPI) in terms of the numbers of nodes visited, constraints checked, and solution bundles generated by comparing it, theoretically and empirically, to other search strategies. We show that FC-DNPI is equivalent to search with the Cross Product Representation (FC-CPR) of [Hubbe and Freuder 1992] in terms of the numbers of solution bundles and constraint checks, while it reduces the number of nodes visited. We establish that both strategies are always superior to FC-BT in terms of all three criteria and dynamic bundling is always beneficial. Further, we compare FC-DNPI to the search procedure of [Haselböck 1993], which exploits static, pre-computed interchangeability relations. We show that the former never generates more solution bundles nor expands more nodes than the latter, and often reduces the number of constraint checks. We also propose, without evaluating them, amendments to the strategy of [Haselböck 1993] to improve its performance and reduce the number of constraint checks

An Efficient Consistency Algorithm for the Temporal Constraint Satisfaction Problem

Dechter et al. [5] proposed solving the Temporal Constraint Satisfaction Problem (TCSP) by modeling it as a meta-CSP, which is a finite CSP with a unique global constraint. The size of this global constraint is exponential in the number of time points in the original TCSP, and generalized-arc consistency is equivalent to finding the minimal network of the TCSP, which is NP-hard. We introduce _AC, an efficient consistency algorithm for filtering the meta-CSP. This algorithm significantly reduces the domains of the variables of the meta-CSP without guaranteeing arc-consistency. We use _AC as a preprocessing step to solving the meta-CSP. We show experimentally that it dramatically reduces the size of a meta-CSP and significantly enhances the performance of search for finding the minimal network of the corresponding TCS

Improving No-Good Learning in Binary Constraint Satisfaction Problems

Conflict-Directed Backjumping (CBJ) is an important mechanism for improving the performance of backtrack search used to solve Constraint Satisfaction Problems (CSPs). Using specialized data structures, CBJ tracks the reasons for failure and learns inconsistent combinations (i.e., no-goods) during search. However, those no-goods are forgotten as soon as search backtracks along a given path to shallower levels in the search tree, thus wasting the opportunity of exploiting such no-goods elsewhere in the search space. Storing such no-goods is prohibitive in practice because of space limitations. In this thesis, we propose a new strategy to preserve all no-goods as they are discovered and to reduce them into no-goods of smaller sizes without diminishing their pruning power. We show how our strategy improves the performance of search by exploiting the no-goods discovered by CBJ, and saves on storage space by generalizing them

A Partial Taxonomy of Substitutability and Interchangeability

Substitutability, interchangeability and related concepts in Constraint Programming were introduced approximately twenty years ago and have given rise to considerable subsequent research. We survey this work, classify, and relate the different concepts, and indicate directions for future work, in particular with respect to making connections with research into symmetry breaking. This paper is a condensed version of a larger work in progress.Comment: 18 pages, The 10th International Workshop on Symmetry in Constraint Satisfaction Problems (SymCon'10

A Constraint-Based Approach to Solving Minesweeper

·Motivate the students for the study of Constraint Processing (CP). Minesweeper is perfect to this end because it allows us to illustrate the use of CP algorithms in a familiar context and show how they operate. ·Understand and demystify humans’ fascination with puzzles. ·Discourage graduate students from losing too much time playing the game by making a program that plays the game for them

Neighborhood Interchangeability and Dynamic Bundling for Non-binary CSPs

1. Interchangeability: An algorithm for computing interchangeability in non-binary CSPs. 2. Dynamic bundling: Integration of the above with backtrack search for solving non-binary CSPs. 3. Experiments demonstrating the benefits of dynamic bundling ·Finding multiple, robust solutions. ·Decreasing computational cost of search

Multi-Dimensional Models Facilitate Automatic Reformulation: The Case Study of the SET Game

In this paper we describe a reformulation strategy for solving multidimensional Constraint Satisfaction Problems (CSPs). This strategy operates by iteratively considering, in isolation, each one of the uni-dimensional constraints in the problem, and exploits the approximate symmetries induced by the selected constraint on the domains in order to enforce this constraint on the simplified problem. We use the game of SET, a combinatorial card game, as a toy problem to motivate our strategy and to explain and illustrate its operation. However, we believe that our approach is applicable to more complex domains of scientific and industrial importance, and deserves more thorough investigations in the future. Our approach sheds a new light on the dynamic reformulation of multidimensional CSPs. Importantly, it advocates that modeling tools for Constraint Programming should allow the user to specify the constraints directly on the attributes of the domain objects (i.e., variables and values) so that their multi-dimensionality can be exploited during problem solving

Neighborhood Interchangeability and Dynamic Bundling for Non-binary CSPs

1. Interchangeability: An algorithm for computing interchangeability in non-binary CSPs. 2. Dynamic bundling: Integration of the above with backtrack search for solving non-binary CSPs. 3. Experiments demonstrating the benefits of dynamic bundling ·Finding multiple, robust solutions. ·Decreasing computational cost of search